Mathematical device.



No. 736,481. a PATENTED AUG. 18, 1903. s. N. BETTS. MATEEMATIGAL DEVICE.

l11131 L10AT111E FILED 1111.5. 1903.

No MODEL.

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UNITED STATES rammed August 1e, 19ers.

PATENT OFFICE.

MATH EMATICAL D.Ev|oE.

SPECIFICATION forming part of Letters Patent No. 736,481, dated August18, 1903. Application filed January 5. 1903. Serial Fo. 18 7,984. (Nomodeld T all whom it may concern.-

Be it known that I, STEPHEN N. BETTs, of the cityV of Hillsdale, in thecounty of Hillsdale and State of Michigan, have invented a new anduseful device which I call the Supervisors Assistant, of which thefollowing is a specification.

'This invention relates to an improved mathematical instrumentespecially designed to assist supervisors in making out or extendingtheir assessment-rolls, and has for its object to provide a simple,inexpensive, and eflicient device of this character by means of whichState; county, and town taxes may be quickly and accurately obtained onindividual valuations.

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In the accompanying drawings, Figure 1 .is

a top plan view of my improved mathematicaly In the accompanyingdrawings, A will b ereferred to as the xed part, andB, B', B", and B asthe rotatable disks or circles. The disks B, B', B", and B'" arerotatably' mounted on a pin or bolt D, secured in any suitable manner tothe fixed part A, and encircling the bolt D andresting on the Adisk B"'is a grooved collar or eyelet E, loosely mounted in an arm or pointer C,a clamping-nut F engaging the threaded end of the bolt D and holding theseveral parts together. By having the arm C loosely mounted on theeyelet E said arm is free to revolve when the clamping-nut is tightened,while the disks remain relatively iixed, thereby permitting said arm tobe swung to any position on the face of the instrument and in alinementwith any desired series of graduations en the disks and xed part A, sothat'the results may be easily read. The figures on the xedpart A andrevolving disks are logarithmically arranged according to the law ot'decimal notation and are relatively alike, varying only by being alittle closer together as the diameter of the disks diminish, the largefigures 1, 2, 3, &c., upto 10occ urring in regular order with varyingspacesbetween them and exactly coveringthe circuit of the disksorcircles. The spaces between the lines decrease in logarithmic ratio, thespace from l to 2 being exactly the same as from 2 to 4 or from 4 to 8,and so on in the same geometrical ratio.

In extending the assessment-rollv we consider the figures on the fixedpart Aas multiplicand's and those on the disks or circles products.opposite to the figure l on the fixed part is the multiplier, no matterwhat that number may be, and each number on the fixed part is multipliedby that number and the product indicatedl on the circle or disk directlyopposite. In dividing, place the divisor found on the disk opposite thenumeral The figure on the circle or disk- 1 on the fixed part.' Thenfind the divil dend on the disk, and opposite to it on the fixed part'will be found the quotient.

The operation of the instrument is as fol` lows: To'ext'end theassessment-roll, three. disks or circlesl are used in order to obtain.the State, county, and town tax at the samev tax on the dollar for thetownship on the disk B", which we Will suppose to be .00865, and alsoplace it opposite the numeral .1 on the fixed part. After'the aboveratio on each disk has been arranged opposite the numeral 1 on the fixedpart the clamping-nut F is tightened, which securely holds the severaldisks in position, the arm C, however, being free to revolve in theeyelet D. The taxon" any individual valuation may now be obtained bysliding the arm C on the pivot D to the numeral on the fixed partrepresenting said valuatiomwhen the State', county, and town tax may beeasily read ou the disks B, B', andB", respectively.- For instance, ifthe valuation is eleven hundred dollars we slide the arm C toa positionin line with the graduation 11, (which we now call eleven hundred,) andby reading across the-circles or disks we nd the State tax to be tendol' lars and twenty-nine cents, the county tax four dollars and ninetycents, and the town tax nine dollars and fifty-two cents. valuationfound on the fixed part the tax on For any that particular valuationwill be found on the cnlating-tables, a grooved collar slidably circleor disk opposite. mounted on the pin and befftring.;` against the Havingthus described the invention, what disks, au arm loosely mounted in thegroove I claim, and desire to secure by Letters Paton said collarandanutengaging the threaded end of the pin and adapted to clamp the col- 15 5ent, is

In a mathematical instrument the combilar on the disks independently ofthe arm. `nation with a frame, of a pin provided with STEPHEN N. BETTS.

terminal threads secured to the frame, a plu- Witnesses: ral-ity ofconcentric disks rotatably` mounted JACOB W. PAENNS, lo on the pin, saidframe and disks bearing cal- MARTIN WILLMAN.

